We use a new approach to derive dielectric mixing rules for macroscopically homogeneous and isotropic multicomponent mixtures of anisotropic inhomogeneous dielectric particles. Two factors of anisotropy are taken into account, the shape of the particles and anisotropy of the dielectric parameters of the particles' substances. Our approach is based upon the notion of macroscopic compact groups of particles and the procedure of averaging of the fields over volumes much greater than the typical scales of these groups. It enables us to effectively sum up the contributions from multiple interparticle reemission and short-range correlation effects, represented by all terms in the infinite iterative series for the electric field strength and induction. The expression for the effective permittivity can be given the form of the Lorentz-Lorenz type, which allows us to determine the effective polarizabilities of the particles in the mixture. These polarizabilities are found as integrals over the regions occupied by the particles and taken of explicit functions of the principal components of the permittivity tensors of the particles' substances and the permittivity of the host medium. The case of a mixture of particles of the ellipsoidal shape is considered in detail to exemplify the use of general formulas. As another example, Bruggeman-type formulas are derived under pertinent model assumptions. The ranges of validity of the results obtained are discussed as well.
The Landau-Lifshitz/Looyenga dielectric mixture expression and its self-similar fractal nature
本文从谱密度表示法的角度讨论了混合介质的介电常数。推导出用于预测介电性质的不同表示[Tuncer E 2005 J. Phys. Condens.事项17 L125]。为了说明该表示的强度并证实所提出的假设，选择Landau-Lifshitz/Looyenga表达式，并提取混合物的结构信息。最近开发的数值方法来解决逆积分变换和建议的经验缩放介电常数表达式估计的谱密度函数的Landau-Lifshitz/Looyenga表达式。在模拟中，夹杂物相的浓度q是变化的。不同夹杂物浓度组成的混合物的估计的谱函数显示出相似的谱密度函数，由一对钟形分布组成，具有重合的峰位置。因此，我们认为，巧合是一个自相似的分形性质的混合物拓扑（结构）的考虑Landau-Lifshitz/Looyenga表达式的一个绝对说明。因此，光谱没有改变显着增加填料浓度水平-表现出自相似的光谱密度函数为不同的浓度水平。我们的结论是，因此，Landau-Lifshitz/Looyenga表达式适用于复杂的复合系统，其结构中有层次的顺序，这证实了文献中的发现。
Evidence for anisotropic dielectric properties of monoclinic hafnia using high-resolution TEM valence electron energy-loss spectroscopy and ab initio time-dependent density-functional theory
